Liquid crystal retarders are increasingly utilized within optical devices such as tunable filters, amplitude modulators and light shutters. Planar aligned smectic liquid crystal devices function as rotative waveplates wherein application of an electric field rotates the orientation of the optic axis but does not vary the birefringence. In contrast, homeotropically aligned smectic liquid crystals, homogeneous aligned nematic devices, and nematic .pi.-cells function as variable retarders, wherein application of an electric field varies the birefringence. Chromaticity is a property of birefringent elements, passive and liquid crystal. There are two main components to chromaticity: (1) dispersion, which is the change in the birefringence (.DELTA.n) with wavelength .lambda.; and (2) the explicit dependence of retardance on 1/.lambda. due to the wavelength dependent optical pathlength. Both components contribute to increased birefringence with decreased wavelength. A birefringent material having a particular retardance at a design wavelength has higher retardance at shorter wavelengths and lower retardance at longer wavelengths. Chromaticity places limitations on the spectral operating range of birefringent optical devices.
Chromaticity compensation for passive retarders was addressed by S. Pancharatnam, Proc. Indian Acad. Sci. A41, 137 [1955], and by A. M. Title, Appl. Opt. 14, 229 [1975], both of which are herein incorporated by reference in their entirety. The wavelength dependence of passive birefringent materials can be reduced by replacing single retarders with compound retarders. The principle behind an achromatic compound retarder is that a stack of waveplates with proper retardance and relative orientation can be selected to produce a structure which behaves as a pure retarder with wavelength insensitive retardance. Pancharatnam showed, using the Poincare sphere and spherical trigonometry, that such a device can be implemented using a minimum of three films of identical retarder material. A Jones calculus analysis by Title (supra) verified the conditions imposed on the structure in order to achieve this result: (1) the requirement that the composite structure behave as a pure retarder (no rotation) forces the input and output retarders to be oriented parallel and to have equal retardance; and (2) first-order stability of the compound retarder optic axis and retardance with respect to wavelength requires that the central retarder be a half-wave plate. These conditions yield design equations that determine the retardance of the external elements and their orientation relative to the central retarder for a particular achromatic retardance. Because these design equations specify a unique orientation of the central retarder and a unique retardance for the external retarders, they have never been applied to active liquid crystal devices and the problem of active retarder chromaticity remains.
For the specific example of an achromatic half-wave retarder, the design equations dictate that the external retarders are also half-wave plates and that the orientation of the external retarders relative to the central retarder is .pi./3. By mechanically rotating the entire structure, wavelength insensitive polarization modulation is feasible. Furthermore, Title showed that the compound half-wave retarder can be halved, and one section mechanically rotated with respect to the other half to achieve achromatic variable retardance. Electromechanical rotation of such compound half-wave retarders has been used extensively to tune polarization interference filters for astronomical imaging spectrometers.
The primary application of ferroelectric liquid crystals (FLCs) has been shutters and arrays of shutters. In the current art, on- and off-states of an FLC shutter (FIG. 1) are generated by reorienting the optic axis of FLC retarder 10 between .pi./4 and 0 with respect to bounding crossed or parallel polarizers 20 and 22. In the off-state, x-polarized light is not rotated by the liquid crystal cell and is blocked by the exit polarizer. In the on-state the polarization is rotated 90.degree. and is therefore transmitted by the exit polarizer.
For maximum intensity modulation, the cell gap is selected to yield a half-wave retardance at the appropriate design wavelength. The on-state transmission of x-polarized light is theoretically unity at the design wavelength, neglecting absorption, reflection and scattering losses. At other wavelengths the transmission decreases. The ideal transmission function for an FLC shutter as in FIG. 1 is given by ##EQU1## where .delta. is the deviation from half-wave retardance with wavelength. This expression indicates a second-order dependence of transmission loss on .delta.. The off-state transmission is in principle zero, but in practice it is typically limited to less than 1000:1 due to depolarization by defects, the existence of multiple domains having different alignments, and fluctuations in the tilt-angle with temperature.
High transmission through FLC shutters over broad wavelength bands is feasible for devices of zero-order retardance, but it is ultimately limited by the inverse-wavelength dependence of retardation and the rather large birefringence dispersion of liquid crystal materials. For instance, a visible FLC shutter device that equalizes on-state loss at 400 nm and 700 nm requires a half-wave retarder centered at 480 nm. A zero-order FLC device with this retardance, using typical FLC birefringence data, has a thickness of roughly 1.3 microns. The transmission loss at the extreme wavelengths, due to the departure from half-wave retardance, is approximately 40%. This significantly limits the brightness of FLC displays and the operating band of FLC shutters and light modulators. In systems incorporating multiple FLC devices, such as tunable optical filters or field-sequential display color shutters, this source of light loss can have a devastating impact on overall throughput and spectral purity.